[1] 柯熙政, 王姣. 涡旋光束的产生、传输、检测及应用[M]. 北京: 科学出版社, 2018.

    Ke X Z, Wang J. Generation, transmission, detection and application of vortex beams[M]. Beijing: Science Press, 2018.

[2] Chen R S, Wang J H, Zhang X Q, et al. Fiber-based mode converter for generating optical vortex beams[J]. Opto-Electronic Advances, 2018, 1(7): 180003.

[3] Gibson G, Courtial J, Padgett M J, et al. Free-space information transfer using light beams carrying orbital angular momentum[J]. Optics Express, 2004, 12(22): 5448–5456.

[4] Wei S B, Wang D P, Lin J, et al. Demonstration of orbital angular momentum channel healing using a Fabry-Pérot cavity[J]. Opto-Electronic Advances, 2018, 1(5): 180006.

[5] 吕宏, 柯熙政. 具轨道角动量光束用于光通信编码及解码研究[J]. 光学学报, 2009, 29(2): 331–335.

    Lv H, Ke X Z. Research on the beam with orbital angular momentum used in encoding and decoding of optical communication[J]. Acta Optica Sinica, 2009, 29(2): 331–335.

[6] Yue Y, Bozinovic N, Ren Y X, et al. 1.6-Tbit/s muxing, transmission and demuxing through 1.1-km of vortex fiber carrying 2 OAM beams each with 10 wavelength channels[C]//Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, 2013.

[7] Ren Y X, Huang H, Xie G D, et al. Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing[J]. Optics Letters, 2013, 38(20): 4062–4065.

[8] Malik M, O’Sullivan M, Rodenburg B, et al. Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding[J]. Optics Express, 2012, 20(12): 13195–13200.

[9] 陈斐楠, 陈晶晶, 赵琦, 等. 高阶贝塞尔高斯光束在非柯尔莫哥诺夫大气中的传输特性[J]. 中国激光, 2012, 39(9): 913001.

    Chen F N, Chen J J, Zhao Q, et al. Properties of high order bessel gaussian beam propagation in non-kolmogorov atmosphere turbulence[J]. Chinese Journal of Lasers, 2012, 39(9): 913001.

[10] 江月松, 张新岗, 王帅会, 等. 部分相干贝塞尔高斯光束在非柯尔莫哥诺夫湍流中的传输特性[J]. 光子学报, 2014, 43(1): 101001.

    Jang Y S, Zhang X G, Wang S H, et al. Propagation of partially coherent bessel-gaussian beams in non-kolmogorov turbulence[J]. Acta Photonica Sinica, 2014, 43(1): 101001.

[11] 柯熙政, 王超珍. 部分相干涡旋光束在大气湍流中传输时的光强分布[J]. 激光与光电子学进展, 2016, 53(11): 110604.

    Ke X Z, Wang C Z. Intensity distribution of the partially coherent vortex beams propagating in atmospheric turbulence[J]. Laser & Optoelectronics Progress, 2016, 53(11): 110604.

[12] 柯熙政, 王超珍. 部分相干离轴涡旋光束在大气湍流中的光强分布[J]. 光学学报, 2017, 37(1): 0101005.

    Ke X Z, Wang C Z. Intensity distribution of partially coherent off-axis vortex beam propagating in atmospheric turbulence[J]. Acta Optica Sinica, 2017, 37(1): 0101005.

[13] Paterson C. Atmospheric turbulence and orbital angular momentum of single photons for optical communication[J]. Physical Review Letters, 2005, 94(15): 153901.

[14] Anguita J A, Neifeld M A, Vasic B V. Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link[J]. Applied Optics, 2008, 47(13): 2414–2429.

[15] Tyler G A, Boyd R W. Influence of atmospheric turbulence on the propagation of quantum states of light carrying orbital angular momentum[J]. Optics Letters, 2009, 34(2): 142–144.

[16] Zhang Y X, Cang J. Effects of turbulent aberrations on probability distribution of orbital angular momentum for optical communication[J]. Chinese Physics Letters, 2009, 26(7): 074220.

[17] 黎芳, 唐华, 江月松, 等. 拉盖尔-高斯光束在湍流大气中的螺旋谱特性[J]. 物理学报, 2011, 60(1): 014204.

    Li F, Tang H, Jiang Y S, et al. Spiral spectrum of laguerre-gaussian beams propagating in turbulent atmosphere[J]. Acta Physica Sinica, 2011, 60(1): 014204.

[18] Torner L, Torres J P, Carrasco S. Digital spiral imaging[J]. Optics Express, 2005, 13(3): 873–881.

[19] 黎芳. 涡旋光束在中强度湍流大气中的传输特性[J]. 激光与光电子学进展, 2013, 50(7): 070101.

    Li F. Propagation characteristics of optical vortices beam in intermediate fluctuation turbulent atmosphere[J]. Laser & Optoelectronics Progress, 2013, 50(7): 070101.

[20] Cheng M J, Guo L X, Li J T, et al. Propagation of an optical vortex carried by a partially coherent laguerre–gaussian beam in turbulent ocean[J]. Applied Optics, 2016, 55(17): 4642–4648.

[21] Zhang W Y, Kuzyk M G. Effect of a thin optical Kerr medium on a laguerre-gaussian beam[J]. Applied Physics Letters, 2006, 89(10): 101103.

[22] 丁攀峰. 整数与分数阶涡旋光束相位奇点的稳定性分析[J]. 华中科技大学学报(自然科学版), 2011, 39(5): 118–122.

    Ding P F. Stabilization analysis of phase singularity of vortex beams with integral and fractional orders[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2011, 39(5): 118–122.

[23] He H, Friese M E J, Heckenberg N R, et al. Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity[J]. Physical Review Letters, 1995, 75(5): 826–829.

[24] Gradshteyn I S, Ryzhik I M. Table of Integrals, Series, and Products[M]. New York: Academic Press, 2014.

[25] 王立瑾, 李强, 魏宏刚, 等. 大气湍流随机相位屏的数值模拟和验证[J]. 光电工程, 2007, 34(3): 1–4, 9.

    Wang L J, Li Q, Wei H G, et al. Numerical simulation and validation of phase screen distorted by atmospheric turbulence[J]. Opto-Electronic Engineering, 2007, 34(3): 1–4, 9.

[26] 邹丽, 赵生妹, 王乐. 大气湍流对轨道角动量态复用系统通信性能的影响[J]. 光子学报, 2014, 43(9): 0901001.

    Zou L, Zhao S M, Wang L. The effects of atmospheric turbulence on orbital angular momentum-multiplexed system[J]. Acta Photonica Sinica, 2014, 43(9): 0901001.

[27] 王飞, 余佳益, 刘显龙, 等. 部分相干光束经过湍流大气传输研究进展[J]. 物理学报, 2018, 67(18): 184203.

    Wang F, Yu J Y, Liu X L, et al. Research progress of partially coherent beams propagation in turbulent atmosphere[J]. Acta Physica Sinica, 2018, 67(18): 184203.

[28] 彭浩. 随机并行梯度下降波前控制算法研究[D]. 长沙: 国防科学技术大学, 2008.

    Peng H. Research of the sotchastic parallel gradient descent algorithm for wavefront control technique[D]. Changsha: National University of Defense Technology, 2008.

[29] Lane R G, Glindemann A, Dainty J. Simulation of a Kolmogorov phase screen[J]. Waves in Random Media, 1992, 2(3): 209–224.